Title
A theory for time-dependent solvation structure near solid-
liquid interface.
Author(s)
Iida, Kenji; Sato, Hirofumi
Citation
The Journal of chemical physics (2012), 136(24)
Issue Date
2012-06
URL
http://hdl.handle.net/2433/159727
Right
© 2012 American Institute of Physics
Type
Journal Article
Textversion
publisher
A theory for time-dependent solvation structure near solid-liquid interface
Kenji Iida and Hirofumi SatoCitation: J. Chem. Phys. 136, 244502 (2012); doi: 10.1063/1.4729750 View online: http://dx.doi.org/10.1063/1.4729750
View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v136/i24 Published by the American Institute of Physics.
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THE JOURNAL OF CHEMICAL PHYSICS 136, 244502 (2012)
A theory for time-dependent solvation structure near solid-liquid interface
Kenji Iida and Hirofumi Satoa)Department of Molecular Engineering, Kyoto University, Kyoto 615-8510, Japan (Received 29 March 2012; accepted 2 June 2012; published online 25 June 2012)
We propose a theory to describe time-dependent solvation structure near solid-liquid interface. Re-cently, we have developed two-dimensional-reference interaction site model to describe solvation structure near solid-liquid interface at the equilibrium state. In the present study, the theory is extended to treat dynamical aspect of the solvation; site-site Smoluchowski-Vlasov equation and surrogate Hamiltonian description are utilized to deal with the time-dependency. This combina-tion enables us to access a long-time behavior of solvacombina-tion dynamics. We apply the theory to a model system consisting of an atomistic wall and water solvent, and discuss the hydration struc-ture dynamics near the interface at the molecular-level. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729750]
I. INTRODUCTION
Solvation dynamics near solid-liquid interface has been extensively studied for a long time. Studies using cyclic voltammetry and impedance spectroscopy have shown that dynamical behavior of solution is crucial to understand chem-ical process near the interface.1–3 According to a recent de-velopment of experimental methods, the dynamics has been revealed at the molecular-level.4–16 For example, McGuire and Shen investigated vibrational dynamics of water near the interface of silica with time-resolved sum-frequency vibra-tional spectroscopy.11 Yamakata and Osawa investigated the dynamics of water molecules on CO-covered Pt electrode us-ing laser-induced temperature jump method.13
Theoretical and computational methods also provide valuable insights by usually considering a solid as an atom-istic wall. Molecular dynamics (MD) simulation is a represen-tative of the methods, and the molecular-level knowledge that cannot be obtained with the experimental methods, has been accumulated.17–21 Time-dependent density functional theory has been also successfully applied to investigate the solva-tion dynamics.22,23Senapati et al. studied the polarization re-laxation of liquid consisting of dipolar hard sphere near the interface by the theory.24–26 Reference interaction site model (RISM) theory is a statistical mechanics for molecular liquids, and can be regarded as an alternative to MD simulation.27–31 One of the differences from MD simulation is that the RISM theory analytically treats an ensemble of infinite number of solvent molecules. In other words, the RISM theory is free from the so-called sampling problem. The theory has been successfully applied to solvation of various systems such as hydration of protein.29,32–40 Recently, we proposed a two-dimensional (2D)-RISM theory for solvation structure near solid-liquid interface at the equilibrium state.41
Although original RISM is a theory for static prop-erty, related theories to describe solvation dynamics are also available. Site-site Smoluchowski-Vlasov (SSSV) equation,
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. FAX:+81-75-383-2799.
which is essentially a diffusion equation for molecular liq-uid, is solved utilizing the solution of the RISM theory.42,43 The equation has been successfully applied to describe the van Hove time correlation function of pure solvents such as water and acetonitrile. The linear response theory is applica-ble to the non-equilibrium state using time correlation func-tion of the equilibrium state.30,44Raineri and co-workers pro-posed surrogate Hamiltonian description, which is regarded as an extended linear response theory.45–47The theory is also solved using the solution of RISM theory and is guaranteed that the state appropriately converges to the final equilibrium state at t (time)→ ∞. The theory is thus accessible to long-time solvation dynamics, which is one of the remarkable ad-vantages compared to MD simulation. The surrogate Hamil-tonian description requires the van Hove function as input. Ishida et al. utilized the SSSV equation to obtain the van Hove function and applied the surrogate description to solvation dy-namics around benzonitrile and pyridinium N-phenoxide after the vertical excitation.48,49 In this study, we propose a theory to treat solvation dynamics near solid-liquid interface. This theory utilizes the surrogate Hamiltonian description and the SSSV equation. The remarkable feature of the theory is to treat the solvation dynamics as time-dependent 2D density distribution, which focuses on the anisotropic solvation struc-ture near the interface.
In Sec. II, we first briefly explain the 2D-RISM theory that describes the 2D density distribution in the equilibrium state, because its solution is required to treat solvation dy-namics. Note that the original 2D-RISM theory is applica-ble only for static properties, and the time-dependency cannot be treated. We then propose a new formula to describe the time-dependent 2D density distribution based on the surro-gate Hamiltonian description. To obtain the van Hove func-tion required as an input in the proposed formula, the SSSV equation is employed. Thanks to their analytical feature, dis-tribution function at arbitrary time t is available with the same computational cost. We apply the proposed theory to the sys-tem in which an atomistic wall is immersed in water solvent. Solvation dynamics near the wall-water interface is discussed at the atomic-level.
244502-2 K. Iida and H. Sato J. Chem. Phys. 136, 244502 (2012)
FIG. 1. Cylindrical coordinate system.
II. THEORY A. 2D-RISM theory
The 2D-RISM theory describes the 2D density distribu-tion near the interface in an equilibrium state. Since a detailed explanation of the theory is given in the previous paper,41 only the essential points are summarized. The 2D distribution function is expressed with the cylindrical coordinate system shown in Fig.1. An origin of the coordinate system is defined as a position of an arbitrary site α in the wall. An axis perpen-dicular to the wall is z axis, ρ is distance from the z axis on a plane parallel to the wall, and φ is an angle along the wall. In this coordinate system, the position of a solvent site η (rη) is treated with a vector rαη(= rη− rα)= {ραη, zαη, φαη}, where
rαis the position of wall site α.
Using the analogous procedure to derive RISM equation,29–31 2D-RISM equation in the reciprocal (k) space is given as follows:41 hαη(kρ, kz)= αη wαα(kρ, kz) ˜cαη(kρ, kz) ×ωVηη(|k|) + n VhV ηη(|k|) , (1)
where kρand kzare the ρ- and z-components of k. h αηis the 2D total correlation function between sites α and η, cαη is the 2D direct correlation function between sites α and η, ωVηη is the intramolecular correlation function of solvent, and hV
ηη is the site-site total correlation function of bulk solvent. ωVηη and hV
ηηhave the same meanings as those used in the original RISM equation.27–31w
ααin Eq.(1)is the 2D-intramolecular
correlation function of the wall written as wαα(kρ, kz)= eik
z·z ααJ
0(kρραα), (2) where J0is the 0th Bessel function.
As seen from Eq.(1), the equation to be solved is a ma-trix equation whose mama-trix size is dependent on the number of wall sites. But the size is drastically reduced by combin-ing with polymer-RISM equation.32–36 Each unit of the wall is here labeled asαi(i= 1, . . . , N) consisting of a finite set of atomic sites{αi, αi, . . ., α
(M)
i }. If respective units are equiva-lent to each other, Eq.(1)is rewritten as
hαη(kρ, kz)= αη Wαα(k ρ, kz ) ˜cαη(k ρ, kz ) ×ωηVη(|k|) + n VhV ηη(|k|) , (3)
where the subscript i is omitted from ˜cαiη and hαiη because
of the identity, and the summation over the units is required only once to obtain the new intramolecular correlation func-tion Wαα given as Wαα(k ρ, kz )= 1 N N ij wαiαj(k ρ, kz ). (4)
To relate the two unknown functions in Eq.(3), ˜cαηand hαη, the following KH-type closure29,38is adopted:
gαη(ραη, zαη)= expχαη(ραη, zαη) for χαη(ραη, zαη)≤ 0 χαη+ 1 for χαη(ραη, zαη) > 0 (5) χαη(ραη, zαη)= −βuαη(ραη, zαη)+ hαη(rαη, zαη)− ˜cαη(ραη, zαη),
where gαη(ραη, zαη)= hαη(ραη, zαη)+ 1 is a 2D pair correla-tion funccorrela-tion (2D-PCF) between the wall site α and the sol-vent site η, β = 1/kBT, kBis Boltzmann’s constant, and uαηis the interaction potential between α and η given as the sum of coulombic and Lennard-Jones terms.
B. Extension to time-dependent solvation structure
Solvation dynamics treated in this study is as follows. At time t < 0, the solvent is in equilibrium with the wall in a pre-cursor state (P). At t= 0, the wall state is suddenly changed from P to a successor state (S), for example, by charging the wall. The solvent responds to the P→ S transition, and re-laxes to the new equilibrium state. The dynamical response
of solvent is here described by the time-dependent 2D-PCF (gαη(ραη, zαη, t)) with the surrogate Hamiltonian description. Since the framework of surrogate Hamiltonian descrip-tion for 1D distribudescrip-tion funcdescrip-tion has been already described in detail by Raineri and co-workers,45–47we here omit the de-tails of derivation. In the surrogate Hamiltonian description, the distribution function of solvent in an equilibrium state is assumed to be described by a linear equation with respect to a wall-solvent coupling δ ˆD,
fD() = fV()[1 − βδ ˆD], (6) where superscript D is P or S, is a set of coordinates and momenta of solvent sites, and fD() is the distribution func-tion in the presence of the wall at the state D. fV() is the distribution function of bulk solvent (i.e., in the absence of
244502-3 K. Iida and H. Sato J. Chem. Phys. 136, 244502 (2012)
the wall), and δ ˆD is written as
δ ˆD = ˆD− dfV() ˆD, (7) ˆ D = 1 (2π )3 dk αη nVhˆαη(k)ψαηD(−k). (8) In Eq.(7), the second term of the right-hand side is vanished because fV() does not depend on ˆD. ˆhαη(k) in Eq.(8)is given as ˆ hαη(k)= 1 nV i eik·rαηi − (2π)3nVδ (k) , (9)
where rαηi = rηi − rα, and rηi is the position of site η of ith
solvent molecule.
Based on Eq.(6), the non-equilibrium ensemble average of a dynamical variable ˆG(t) in the condition of P → S transi-tion at t= 0 is given as45–47
ˆG(t) =
df (, t) ˆG(t) = ˆGS + βC(t), (10)
where f (, t) is the time-dependent distribution function of solvent, and
ˆGD =
dfD() ˆG (11)
is the ensemble average of static variable ˆG in the equilibrium state D (= P or S). C(t) is the time correlation function defined as
C(t)=
dfV() ˆG(t)(δ ˆS− δ ˆP). (12) Notice that ˆD or ψαηD (cf. Eq.(8)) is not yet explicitly given. If ˆD is given as the factual interaction energy between the wall and solvent, such as the sum of coulombic and Lennard-Jones terms, then the standard linear response formula is yielded.45 In the surrogate Hamiltonian description, ψD
αη is given as the renormalized potential that gives the static aver-age ˆGD
(cf. Eq.(11)) identical to the average given without the assumption of Eq.(6). ψD
αηof the surrogate description for the 2D density distribution function is found from the follow-ing equation: hDαη(kρ, kz)= ˆhαη(k)D ,φαη = αη ek·rαα−βψD αη(k) wVηη(|k|) + n VhV ηη(|k|) φαη , (13)
where · · · φαη denotes the averaging over φαη, and the
as-sumption of Eq.(6)is used. The procedure to derive Eq.(13)
is analogous to that for 1D distribution function hD αη(|k|) (Refs.45–47). If ψD αη(k) in Eq.(13)is defined as −βψD αη(k)= ˜c D αη(k ρ, kz ), (14)
then the same formula as Eq.(1)is obtained. Note that Eq.(1)
is derived without the assumption of Eq.(6), whereas Eq.(13)
is derived using the assumption. Equation (14) is therefore the definition of ψD
αηfor the time-dependent 2D distribution function.
Using Eq.(14), the following equation is derived from Eq.(10): hαη(kρ, kz, t) =hˆαη(k, t) ,φαη = αη wαα(kρ, kz) ˜cSαη(k ρ, kz )ωVηη(|k|) + n VhV ηη(|k|) + wαα(kρ, kz) ˜cSαη(k ρ, kz )− ˜cPαη(k ρ, kz )sηVη(|k|, t). (15) Here, ˆhαη(k, t) in Eq. (15) is defined by rewriting rαηi in
Eq.(9)as rαηi(t) (= rηi(t)− rα), where rηi(t) is the position
of ηiat time t. sηVη(|k|, t) in Eq.(15)is the van Hove function of bulk solvent sVηη(|k|, t) = 1 V dfV()nVhˆη(k, t) ˆhη(−k), (16) where V is the system volume, and ˆhη(k, t) is defined by rewriting rαηi in Eq.(9)as rηi(t).
To calculate sηVη, here we use the SSSV equation,42,43
∂ ∂ts V (|k|, t) = −|k|2DV × [{ωV(|k|)}−1− nV ˜cV(|k|)] · sV(|k|, t), (17)
where sV has the element sV
ηη, DV is the diffusion coefficient, and the matrix elements ofωV and ˜cV are the intramolecular and direct correlation functions of bulk solvent, respectively. The SSSV equation can be analytically solved by using the inverse Laplace transformation for some simple cases such as a triatomic molecule.42
Utilizing the same procedure of deriving Eq. (3) from Eq. (1), Eq.(15)is rewritten to deal with the identity of the
244502-4 K. Iida and H. Sato J. Chem. Phys. 136, 244502 (2012) units as follows: hαη(kρ, kz, t) = αη Wαα(kρ, kz) ˜cSαη(k ρ, kz )ωηVη(|k|) + n VhV ηη(|k|) + Wαα(kρ, kz) ˜cαSη(kρ, kz)− ˜cPαη(kρ, kz) sVηη(|k|, t). (18) Equation(18)is the central equation in this study for the time-dependent 2D distribution near the interface. In the equa-tion, Wαα{˜cSαη− ˜cαPη} describes the perturbation affecting the solvent due to the P→S transition, where the geometrical information of the wall is expressed by Wαα. sV describes the response of solvent to the perturbation.
The procedure of the present theory is as follows. hVηη is calculated with the RISM equation for bulk solvent. The renormalized potentials, ˜cS
αηand ˜cPαη, are calculated with the 2D-RISM theory (Eqs.(3)and(5)). The van Hoff function sηVη at time t is calculated by the SSSV equation (Eq. (17)). Us-ing these obtained functions (hVηη, s
V
ηη, ˜cαSη, ˜cPαη), Eq.(18)is solved, and thereby gαη(ραη, zαη, t) (= hαη(ραη, zαη, t)+ 1) is obtained.
Now, we summarize the features of the present theory. Although the SSSV equation is not appropriate to treat the short-time region (t < 0.1 ps), the SSSV equation analyti-cally yields the van Hove function at arbitrary time t within the same computational cost.42,43In addition, the solution of Eq.(18)converges to the solution of Eq.(3)for the state S at t→ ∞. In other words, the present theory has the advantage in treating the long-time region. It is complementary feature with MD simulation that has an advantage in treating short-time dynamics.
III. COMPUTATIONAL DETAIL
2D Fourier transform to solve the present equation con-sists of the Hankel transform with respect to ρ and 1D Fourier transform with respect to z. The Hankel transform is performed using Talman’s algorithm.50 The number of grid points along ρ is 512 with the spacing of ln (ρ/ρ0)
= 0.02, where ρ0 is 1 bohr. The minimum of ρ, ρmin, is set
to ln (ρmin/ρ0)= −5.12. The number of grid points along z is
4096 with the spacing of z= 0.02 bohr. To apply our theory to a charged wall, Ng’s method51 is employed. These details of the transforms are the same as the previous study.41
The system treated here consists of a single wall im-mersed in water solvent. Atomic sites of the wall are arranged in accord with the face of a cubic lattice. The lattice constant (a) is 1.5 Å and the Lennard-Jones parameters of the atomic sites are σ = 1.500 Å and = 0.101 kcal mol−1.41The num-ber of unit N is set to 625 (= 252). It was checked that the
peak height of distribution is almost unchanged when N is larger than or equal to 625.41 For solvent water molecule, simple point charge like model is employed (oxygen site; σO = 3.166 Å and O = 0.155 kcal mol−1, hydrogen site; σH= 1.000 Å and H= 0.056 kcal mol−1).52 The diffusion coefficient of water is set to 2.3× 10−5cm2s−1, which is the
experimental data.53Calculations are carried out at 298.15 K
and the number density of water solvent of nV = 0.033426 Å−3.
In the following, we rewrite gαη(ραη, zαη, t) as gO(ρ, z, t)
or gH(ρ, z, t) for simplicity, where gO(ρ, z, t) and gH(ρ, z, t)
are time-dependent 2D-PCFs of the wall site–solvent oxygen site and the wall site–solvent hydrogen site, respectively.
IV. RESULTS AND DISCUSSIONS A. Distribution of oxygen
Figure2shows the contour map of gO(ρ, z, t), where each
atomic site of the wall is suddenly charged to−0.04213 |e| at t = 0 s, corresponding to the surface charge density of −0.3 C m−2. The distributions at t= 0 s and t = ∞ s are,
of course, identical to those around the neutral and charged walls, respectively.41The peak at z= 2 Å corresponds to the first solvation shell, and the height is 3.78 (ρ = 0.9 Å and z = 2.0 Å) at t = 0 s. As the time proceeds, the peak becomes slightly higher to 3.86 (t= 1 ps), and finally reaches to 4.01 (t = ∞ s). This peak becomes monotonously higher as the time proceeding. Another maximum at z∼ 5 Å corresponds to the second solvation shell. Similar to the first solvation shell, the distribution also increases as the time proceeds, and the area with gO>1.2 is gradually expanded. These increases of the
Å gO(ρ, z, t) 0.0 2.0 4.0 0.0 1.5 0.0 1.5 0.0 1.5 1 5 0 s 10 fs 100 fs ρ / z / Å 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 1.5 0.0 1.5 1 ps s 0.0 1.5 10 ps
FIG. 2. Contour map of time-dependent 2D-PCFs between wall site and oxy-gen site. From top to bottom, the distributions are at t = 0 s, t = 10 fs,
244502-5 K. Iida and H. Sato J. Chem. Phys. 136, 244502 (2012)
distribution of solvent water in the first and second solvation shells suggest that water molecules tend to be attracted to the wall as the time proceeds. At the short range region (z < 2 Å), distribution with gO<0 (shown by white color) is found. For
example, gOat t= 100 fs has minimum at z = 0 Å, and the
mean value in the core region (z = 0 Å and ρ < 1.5 Å) is −0.2. As shown in the following discussion, gHhas also the
negative value, and the mean value at t = 100 fs in the core region (z= 0 Å and ρ < 0.8 Å) is −0.1. As noted by Raineri et al., this type of artifact could be often observed in analytical solvation-dynamics theory.46 Nishiyama et al. utilized surro-gate description and also discussed the negative value.54,55
B. Distribution of hydrogen
Change of the distribution of hydrogen site clearly shows the formation of ordered solvation structure. Figure 3shows the distribution of solvent hydrogen, gH(ρ, z, t). At t= 0 s,
the peak is found in the area from z= 2.5 Å to 3.0 Å, which is slightly distant from the first solvation shell of the oxygen site (z ∼ 2 Å). gO(ρ, z, t= 0) and gH(ρ, z, t= 0) therefore
show that the hydrogen site tends to be located further from the wall than the bound oxygen.41
As the time proceeds, the distribution is noticeably changed. In particular, the change in the distribution at z ∼ 1 Å is remarkable. Although the distribution remains mostly unchanged just after the charging (t= 10 fs), a small
0.0 1.0 2.0 Å 0.0 1.5 0.0 1.5 0.0 1.5 1 5 0 s 10 fs 100 fs gH(ρ, z, t) z / Å 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 ρ / 0.0 1.5 0.0 1.5 1 ps s 0.0 1.5 10 ps
FIG. 3. Contour map of 2D-PCFs between wall site and hydrogen site. From top to bottom, the distributions are at t= 0 s, t = 10 fs, t = 100 fs, t = 1 ps,
t= 10 ps, t = ∞ s, respectively.
peak appears around t= 100 fs (ρ = 0.79 Å and z = 0.86 Å) and becomes monotonously higher as the time proceeds; gH=0.41 (t = 0 s), 0.55 (t = 10 fs), 0.88 (t = 100 fs), 1.06
(t = 1 ps), 1.08 (t = 10 ps), and finally 1.12 (t = ∞). The change at z∼ 1 Å is mostly complete at t = 1 ps, that is, 92 % of the total change is accomplished until t= 1 ps. The change of distribution indicates that a contribution from another con-figuration (solvation structure) becomes greater, namely, one of the O−H bonds is directed perpendicular to the wall.41
The distribution of gH(ρ, z, t) found in the area from z
= 5 Å to 6 Å corresponds to the second solvation shell. This distribution also changes as the time proceeds, although the change is small, only about 0.1. Comparing with the distribu-tion at z∼ 1 Å, the change at z ∼ 5 Å is slow. The value at the ridge (ρ= 0.79 Å and z = 5.4 Å are selected) remains almost unchanged until t= 100 fs (gH= 1.16), and then slightly
in-creases to 1.19 (t= 1 ps), 1.21 (t = 10 ps), and 1.25 (t = ∞ s). In contrast to the first shell (z∼ 1 Å), the response in the sec-ond solvation shell is relatively slow, and not completed even at t= 10 ps (only 56%). This difference in solvation dynam-ics would be assigned to that the change of the second shell begins after the change of water orientation in the first shell. Similar dynamical behavior of solvent at some point distant from the interface has been reported in a series of works by Senapati et al., in which the polarization relaxation near the interface was investigated with time-dependent density func-tional theory,24–26as well as with MD simulation.21
V. CONCLUSION
In this study, we proposed a theory for time-dependent solvation structure near solid-liquid interface. The proposed theory is an extension of 2D-RISM theory, which is recently developed by us, and allows to describe the response of sol-vent molecule due to the sudden change of the wall state as the time-dependent 2D density distribution function. To treat the time dependency, the surrogate Hamiltonian description and the SSSV equation are utilized. This utilization enables the theory to access to long-time solvation dynamics.
The solvation dynamics of water solvent near the wall is investigated with the proposed theory. The distribution of oxygen corresponding to the first and second solvation shells increases by charging the wall. More conspicuous change is found in the distribution of hydrogen at z∼ 1 Å. This is as-signed to the orientation of water molecule towards the wall. The distribution of hydrogen corresponding to the second shell shows small and slow change compared to the first shell. It is suggested that the solvation dynamics in the second shell follows the orientation of water molecule in the first solvation shell.
ACKNOWLEDGMENTS
The work is financially supported in part by grant-in-aid for Scientific Research on Priority Areas “Molec-ular Science for Supra Functional Systems” (Grant No. 477-22018016), grant-in-aid for Scientific Research on Inno-vative Areas “Molecular Science of Fluctuations” (Grant No.
244502-6 K. Iida and H. Sato J. Chem. Phys. 136, 244502 (2012)
2006-21107511), as well as by grant-in- aid for Scientific Re-search (C) (Grant No. 20550013). K.I. thanks the grant-in aid for JSPS Fellows. The Strategic Programs for Innovative Re-search (SPIRE), the Computational Materials Science Initia-tive (CMSI), and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan are also acknowl-edged. Theoretical computations were partly performed using Research Center for Computational Science, Okazaki, Japan.
1T. Pajkossy, T. Wandlowski, and D. M. Kolb,J. Electroanal. Chem.414, 209 (1996).
2Z. Kerner and T. Pajkossy,Electrochim. Acta47, 2055 (2002). 3N. M. Markovi´c and P. N. Ross,Surf. Sci. Rep.45, 117 (2002). 4K. Hayamizu and Y. Aihara,J. Phys. Chem. Lett.1, 2055 (2010). 5K. Hayamizu, S. Seki, H. Miyashiro, and Y. Kobayashi,J. Phys. Chem. B
110, 22302 (2006).
6A. Delville and M. Letellier,Langmuir11, 1361 (1995). 7J. F. Smalley and Y.-C. Wu,J. Phys. Chem. C115, 2693 (2011). 8J. F. Smalley,J. Electroanal. Chem.640, 68 (2010).
9H. Miyake, T. Okada, G. Samjeské, and M. Osawa,Phys. Chem. Chem.
Phys.10, 3662 (2008).
10A. Yamakata, T. Uchida, J. Kubota, and M. Osawa,J. Phys. Chem. B110, 6423 (2006).
11J. A. McGuire and Y. R. Shen,Science313, 1945 (2006).
12A. E.-Bafrooei and E. Borguet,J. Am. Chem. Soc.132, 3756 (2010). 13A. Yamakata and M. Osawa,J. Phys. Chem. C112, 11427 (2008). 14H. Noda, K. Ataka, L.-J. Wan, and M. Osawa,Surf. Sci.427, 190 (1999). 15J. O. Bockris, E. Gileadi, and K. Müller,J. Chem. Phys.44, 1445 (1966). 16R. Sadr, M. Yoda, P. Gnanaprakasam, and A. T. Conlisk,Appl. Phys. Lett.
89, 044103 (2006).
17C. Cagle, G. Feng, R. Qiao, J. Huang, B. G. Sumpter, and V. Meunier,
Microfluid. Nanofluid.8, 703 (2010).
18J. Vatamanu, O. Borodin, and G. D. Smith,J. Phys. Chem. B115, 3073 (2011).
19M. R. Warne, N. L. Allan, and T. Cosgrove,Phys. Chem. Chem. Phys.2, 3663 (2000).
20G. Stirnemann, P. J. Rossky, J. T. Hynes, and D. Laage,Faraday Discuss.
146, 263 (2010).
21A. Chandra and S. Senapati,J. Mol. Liq.77, 77 (1998). 22B. Bagchi and A. Chandra,Adv. Chem. Phys.80, 1 (1991). 23B. Bagchi and R. Biswas,Adv. Chem. Phys.109, 207 (1999).
24A. Chandra, S. Senapati, and D. Sudha,J. Chem. Phys.109, 10439 (1998).
25S. Senapati and A. Chandra,Phys. Rev. E.59, 3140 (1999). 26S. Senapati and A. Chandra,J. Chem. Phys.113, 377 (2000). 27D. Chandler and H. C. Andersen,J. Chem. Phys.57, 1930 (1972). 28F. Hirata and P. J. Rossky,Chem. Phys. Lett.83, 329 (1981).
29Molecular Theory of Solvation, edited by F. Hirata (Kluwer, Dordrecht,
2003).
30J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic, London, 2006).
31C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids (Clarendon, Oxford, New York, 1984), Vol. 1.
32D. Chandler, Y. Singh, and D. M. Richardson,J. Chem. Phys.81, 1975 (1984).
33K. S. Schweizer and J. G. Curro,Phys. Rev. Lett.58, 246 (1987). 34J. G. Curro and K. S. Schweizer,J. Chem. Phys.87, 1842 (1987). 35F. Hirata and R. M. Levy,Chem. Phys. Lett.136, 267 (1987). 36R. Akiyama and F. Hirata,J. Chem. Phys.108, 4904 (1998). 37A. Kovalenko and F. Hirata,Chem. Phys. Lett.290, 237 (1998). 38A. Kovalenko and F. Hirata,J. Chem. Phys.110, 10095 (1999).
39S. Woelki, H.-H. Kohler, and H. Krienke,J. Phys. Chem. B111, 13386 (2007).
40S. Woelki, H.-H. Kohler, and H. Krienke,J. Phys. Chem. B112, 3365 (2008).
41K. Iida and H. Sato,J. Chem. Phys.135, 244702 (2011). 42F. Hirata,J. Chem. Phys.96, 4619 (1992).
43F. Hirata, T. Munakata, F. O. Raineri, and H. L. Friedman,J. Mol. Liq.
65/66, 15 (1995).
44H. L. Friedman, A Course in Statistical Mechanics (Prentice Hall, Engle-wood Cliffs, 1985).
45F. O. Raineri, H. Resat, B.-C. Perng, F. Hirata, and H. L. Friedman,
J. Chem. Phys.100, 1477 (1994).
46F. O. Raineri, B.-C. Perng, and H. L. Friedman,Chem. Phys.183, 187 (1994).
47H. L. Friedman, F. O. Raineri, F. Hirata, and B.-C. Perng,J. Stat. Phys.78, 239 (1995).
48T. Ishida, F. Hirata, and S. Kato,J. Chem. Phys.110, 11423 (1999). 49T. Ishida,J. Phys. Chem. B113, 9255 (2009).
50J. D. Talman,J. Comp. Phys.29, 35 (1978). 51K.-C. Ng,J. Chem. Phys.61, 2680 (1974).
52H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, and J. Hermans, in Intermolecular Forces, edited by B. Pullman (Reidel, Dordrecht, 1981). 53K. R. Harris and L. A. Woolf,J. Chem. Soc. Faraday Trans.76, 377 (1980). 54K. Nishiyama, F. Hirata, and T. Okada, Chem. Phys. Lett. 330, 125
(2000).